This work presents a general concept of an intense laser-driven source of strong electromagnetic waves, which can be used for obtaining powerful terahertz radiation with controlled polarization. It is shown that the irradiation of a solid target surface by short relativistic laser pulses at small angles provides the excitation of strong compact relativistic discharge current pulses, propagating in a certain direction. For elliptical targets, this current emits elliptically polarized electromagnetic radiation at a given frequency with the ellipticity and the spectra defined by the target geometry. The proposed setup allows reaching extreme THz intensities and provides easy control of the radiation parameters, making it attractive for various scientific and technological applications.